Microwave filter



Dec. 4, 1951 s B, COHN 2,577,510

MICROWAVE FILTER Filed April 2, 1946 sgYMouR B. coHN ATTORNEY Patented Dec. 4, 1951 MICROWAVE FILTER Seymour B. Cohn. Cambridge, Mass., assigner to the United States of America by the Secretary of War as represented Application April 2, 1946, SerialJNo. 658,939

This invention relates to high frequency transmission line filters and more particularly to low pass coaxial type lters.

Conventional low pass T- or Pi-section lters utilize concentric capacitors as the capacitor elements and sections of the inner conductor of a transmission line as the inductance elements. It is important that the iilters be carefully designed so that the measured pass band response conforms to the calculated response very closely. This is especially desirable in filters for use in the microwave range of frequencies (i. e. having wavelengths of the order of centimeters). This invention has for one of its objects the utilization of distributed line parameters in the design and construction of microwave filters of the above kind, and more particularlypf design criteria 1 Claim. (Cl. 1784-44) l which gives more predictabl'results than thos heretofore used or known.

It is another object of the invention to provide a low-pass lter of transmission line elements whose dimensions may be determined according to this invention.

It is another object of the invention to provide a novel method of predetermining the dimensions of a lter to obtain the desired characteristics of the lter.

For a better understanding of the invention, together with other and further objects thereof, reference is had to the following description, taken in connection with the accompanying drawing, wherein:

Fig. 1 is a schematic diagram of the basic equivalent circuit of a single filter section according to the present invention.

Eig. 2 is a simplied circuit diagram of Fig. 1; an

Fig. 3 is a longitudinal sectional view of a lter constructed according to the present invention.

Fig. 4 is a diagram of a half of the section shown in Fig. 1. .Y

In general, the dlter according to the invention is mechanically similar to the conventional coaxial type low-pass iilter in that it utilizes concentric capacitors as the capacitor elements and lengths of the inner conductor of a transmission line as the inductance elements. Basically, the circuit for a single filter section is shown in Fig. 1 in which It is the `input followed in turn by an end length I I, which may be a length of high impedance coaxial line, by a length of low characteristic impedance line I2, then by a length of v2 l high characteristic impedance sections are indicated by the coils IB in Fig. 2 which act as inductances and in which the low characteristic l impedance sections plus discontinuity capacitancesare shown as the shunt capacitances I1.

The construction of a iilter having four sec- V- tions of the kind indicated in Figs. 1 and 2 is shown in Fig. 3. As shown, the lter 20 comprises a length or section of coaxial conductor line 2| having an inner conductor 22 and an outer concentric conductor 23 which may be inserted in or connected at each end thereof to a section of the usual type of coaxial conductor transmission line, the inner conductor of which is indicated at 24,

4in the circuit of -anelectrical system such as a communication or radio object-locating system.

space between the disk 25v and the outer conductor 23. The disks 25 are disposed at spaced intervals along the length of lter 20 and are positioned in such a manner that they separate, while being in electrical connection with, sections of inner conductor 22 of substantially equal impedance. Thus as shown, the inner conductor 22 comprises a plurality of sections. each sectiony being separated by a .disk 25. The conductor sections 22 comprise the inductance elements and the disks 25 comprise the shunt capacitor elements of the filter 20. Thus, it will be seen that filter 20 comprises a plurality of lter sections. each of which may be either an equivalent T- type section or a 1r-type section.

rating a pair of inner conductor sections 22',

eachsection 22.'V being of substantiallv equal impedance and being of substantially half the length of "a section 22 between adjacent disks 25 off Fig. 3. When the lter is arra-ngedwith the vr-type sections. each 1r-type section comprises a v disk member 25 separated bv a conductor section 22. Thus, the lter sections preferably are arranged so that the lter 2f! comprises short lengths of alternate low and high characteristic impedance transmission line connected in series, 02 and 01, respectively, designating the angular lengths thereof in radians where Z being the physical length in centimeters and 7i being the wavelength of the energy passing As shown in f Fig. 3, the `filter 20 comprises four T-type secthrough-filter 20 in centimeters.

Each T-type section comprises a disk25 sepac 3 tions, the terminations of filter 2U occurring at the center of a high impedance length of the transmission line. ever, that when the filter comprises f-type sections, they are terminated at the center of a low impedance length of line instead of a high impedance line as shown in Fig. 3.

In order to design a. low-pass filter having the desired characteristics, and to obtain the Ydesired results in a more predictable manner, it is preferable that the following design method be followed, where the discontinuity lcapacitance caused by the termination of the E iield on the transverse surfaces of the disk members 25, which will usually be appreciable, is taken into consideration. First, the length of 01e and a tentative length of 02e, which Lneglects the discontinuity capacitance effect, are chosen to have respective values such as to cause spurious responses to fall outside of the desired frequency range. 01e represents the length of the high impedance section of line between adjacent disk members at the cut-off frequency and 02a designates the electrical length of the low impedance line at the cut-off frequency represented by the thickness of each of the disk members 25. The ratio of the characteristic impedances of the sections or lengths of line of disks 25 and the distance between adjacent disks 25 may then be calculated from the formula:

cot 2- tan It then follows that A value of zero frequency characteristic imped` ance Koo is then assumed, then Zm found from the following relationship:

Zox Koo where Ba is the discontinuity susceptance which may ne calculated from the following equation:

Where fo is in megacycles per second, r3 is the' inner radius of the outer conductor of the coaxial line in centimeters, and Cav (an) is the discontinuity capacitance in micro-microfarads per centimeter circumference calculated in accordance with curves given by J. R. Whinnery, H. W. Jamieson, andv Theo Eloise Robbins, Proc. of IRE, vol. 32, 695 (1944).

Thus the lengths of the filter sections designated by the thickness of disks 25 and the spacings between adjacent disks 25 (of line section 22) may becalculated from the electrical lengths 01o and @ze according to the above relations by taking into account the dielectrics used.

It will be understood, how- It has been found that a filter constructed and designed as hereinbefore described has a measured passband response which conforms extremely closely to the calculated response; that is, it is possible according to this invention to design a low-pass filter much more easily and with more predictable results than has heretofore been known.

The derivation of the design formulae used will be made most readily apparent if consideration :is first given kto Fig. 4 which is a schematic diagram of one half the filter section shown in Fig. 1, Where 21 vis ohehalf of I2 and the other numbered elements correspond to those similarly numbered in Fig. 1. The symbols shown below have theV same meaning as given in Formulas 2, 3 and 4. l

B1 and B2 are the respective susceptance of' Zoi and Zoe and Bu is the discontinuity susceptance.

By inspection we see that the mid 0r characteristie impedance, Koi, must be zero at cut-oil, while the mid 62 characteristic impedance, Kaz, must be infinite. Assume terminations on an image basis. Then the lter is matched at every point and hence the following relation holds at cutoff:

B1+B2+Bc=0 (d) Where 1 2. B.- ZM cot 2 (b) Bg-ZM tan 2 Therefore -ot 25+?! an gaze-*0 (d) 02 If Bc is zero,

' v 01e ZI cot 2 (e) Zoz t 02,

which is Equation 1.

With Bc taken into account, 5 cot -g 2c 4 tan BeZo; Zoe

or substituting Equation e tan =tan o-f-BJM 02e 02=2 arctan (tan -BZnz) (y) which is Equation 3, above.

The characteristic impedance is most simply derived by matrix algebra. Since the zero frequency characteristic impedance Koo is of principal interest, Bc will be neglected. The matrix for this half' section is:

performing the matrix multiplication converts this matrix into the form:

E 1 A B E, x I1 C D I2 where A', B', C', D' represent the product terms of the matrix multiplication. Having calculated A', B', C', and D', the respective characteristic impedances Koi and Koz are:

where I is the propagation constant for a whole section.

On performing the indicated operation one obtains for Koi,

6 acteristic impedance portions of said filter; the axial lengths and diameters of the components of said high and low characteristic impedance portions having dimensions dened in accordance with the following formulae:

e a c a 2 cos 2+Z02 cos 2 sin 2)(cos 2 Kaz is the same except that all subscripts are interchanged between corresponding terms.

The zero frequency is:

Z01=Koo This relationship also holds true at the cutoff' frequency so that Z01=Kou (n) which is Equation 2.

While there has been described what is at Dresent considered the preferred embodiment of the invention, it will be obvious to those skilled in the art that various changes and modifications may be made therein without departing from the invention.

What is claimed is:

A low-pass filter of the coaxial type for use within the microwave range of frequencies of electromagnetic energy comprising: concentric inner and outer conductors insulated from each other; said outer conductor being of uniform diameter; said inner conductor comprising alternate sections having respectively first and second diameters; said second diameter being larger than said first diameter; sections of said inner conductor of like diameter having equal axial lengths, whereby the sections of said inner conductor having said first diameter and sections of said outer conductor adjacent thereto form high characteristic impedance portions of said filter and the sections of said inner conductor having said second diameter and sections of said outer conductor adjacent thereto form low charportions, 01e and 02e being so chosen that spurious responses fall outside of the desired lfrequency range. and

z m Zn: is the ratio of the characteristic impedance of each high characteristic impedance portion to the characteristic impedance of each low characteristic impedance portion;

Where Koo is the assumed value of the zero frequency characteristic impedance;

where 02 is the electrical length in radians at the desired cut-off frequency of each of said low characteristics corrected for said discontinuity capacitance and Bc is the susceptance at the desired cut-olf frequency of said discontinuity capacitance; and

REFERENCES CITED The following references are of record in the le of this patent:

UNITED STATES PATENTS Name Date Mason Dec. 12, 1939 Rogers Nov. 26, 1946 OTHER REFERENCES Proceedings I. R. E., vol. 32, No. 11, November 1944 (pages 696-709).

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